Eigenvalues & Eigenvectors of
S*
Circular left-shift operator — after Bamieh (2018), Fig. 4.1
n =
8
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Re/Im plot
Center freqs
eigenvalue ρ
m
eigenvector entries
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For dimension
n = 8
, the eigenvalues of
S*
are the
8th
roots of unity
ρ
m
= e
i·2π·m/n
, and each eigenvector is
w
(m)
= (1, ρ
m
, ρ
m
2
, …, ρ
m
n−1
)
.